Rapid prediction of cell-free layer thickness: A semi-analytical hemorheological model for blood flow in stenosed vessels

Hemodynamic characteristic parameters are closely associated with the onset and progression of cardiovascular diseases. Constructing a hemorheological prior model with complete physical significance remains a critical challenge in this field. In particular, the Fåhraeus–Lindqvist effect and the associated cell-free layer (CFL) in microcirculation are essential for understanding blood flow behavior. This study establishes a constitutive model of blood flow in microvessels based on multiphase flow theory, where flow velocity is expressed as a function of shear rate, and the shear rate is used as the independent variable to analyze flow field structure within circular vessels. By introducing an analytical solution of the velocity field in stenosed vessels in bipolar coordinates, an efficient prediction method for CFL thickness is proposed. Theoretical analysis and numerical simulations demonstrate that within the same vascular cross section, velocity cores exhibit a slight eccentric distribution. Under low-shear conditions, red blood cells tend to form rouleaux aggregates, which are larger in volume and higher in rigidity, limiting their migration toward the vessel wall and leading to CFL thickening. Such aggregation simultaneously reduces disturbance diffusion, thereby enhancing CFL stability and further increasing its thickness. Hematocrit (Hct) is identified as the dominant factor influencing CFL thickness. Shear stress exerts a significant positive effect, with a standardized regression coefficient of 0.1735 and a random forest feature importance of 0.3786, indicating its strong role in promoting CFL formation and development. Although plasma viscosity (μ) has a relatively weaker influence, its effect on CFL thickness demonstrates strong linear interpretability.